A393053 Number of divisors d of n such that d and A276086(n) are coprime, where A276086 is the primorial base exp-function.

1, 2, 1, 3, 2, 4, 2, 4, 1, 2, 2, 6, 2, 4, 1, 5, 2, 6, 2, 3, 2, 4, 2, 8, 1, 4, 1, 6, 2, 8, 2, 6, 2, 4, 2, 9, 2, 4, 2, 4, 2, 4, 2, 6, 1, 4, 2, 10, 1, 2, 2, 6, 2, 8, 2, 4, 2, 4, 2, 12, 2, 4, 1, 7, 4, 8, 2, 6, 2, 2, 2, 12, 2, 4, 1, 6, 2, 8, 2, 5, 1, 4, 2, 6, 2, 4, 2, 8, 2, 12, 2, 6, 2, 4, 4, 12, 2, 2, 2, 3, 2, 8, 2, 8, 1

Offset

1,2

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Index entries for sequences related to primorial base.

Formula

a(n) = Sum_{d|n} [gcd(d,A276086(n)) = 1], where [ ] is the Iverson bracket.

a(n) = A000005(n) - A393054(n).

Prog

(PARI)
A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A393053(n) = { my(x=A276086(n)); sumdiv(n, d, 1==gcd(d, x)); };

Crossrefs

Cf. A000005, A276086, A393054.

Cf. also A393051.

Sequence in context: A360679 A339894 A355140 * A286632 A308453 A286585

Adjacent sequences: A393050 A393051 A393052 * A393054 A393055 A393056

Keyword

nonn,base,easy

Author

Antti Karttunen, Feb 04 2026

Status

approved